# Equation of the Diameter of Parabola Bisecting Parallel Chords of Given Slope

**Problem**

A parabola has an equation of *y*^{2} = 8*x*. Find the equation of the diameter of the parabola, which bisect chords parallel to the line *x* – *y* = 4.

A. y = 2 |
C. y = 4 |

B. y = 3 |
D. y = 1 |

**Answer Key**

[ C ]

**Solution**

From

$m = 1$

*x*–*y*= 4:$m = 1$

Slope of chords:

$y' = m$

$y' = 1$

From the parabola:

$y^2 = 8x$

$2y \, y' = 8$

$2y(1) = 8$

$y = 4$ ← Answer: [ C ]

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